<p>In this paper, we investigate the Bohr–Rogosinski radius for holomorphic mappings on the unit ball of a complex Banach space with values in a higher dimensional complex Banach space. First, we obtain the Bohr–Rogosinski radius for holomorphic mappings with values in the closure of the unit polydisc of the space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1061_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {C}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1061_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. Next, we obtain the Bohr–Rogosinski radius for holomorphic mappings with values in the closure of the unit ball of a <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1061_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {JB}^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>JB</mtext> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-triple. Finally, we obtain the Bohr–Rogosinski radius for a class of subordinations on the unit ball of a complex Banach space. All of the results are proved to be sharp.</p>